Ability Scores

Posted on June 18, 2017

The official D&D 5e rule for generating random ability scores is to
roll four 6-sided dice, total the highest three, and record the
result. This is repeated six times, and the scores are assigned to
Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma
however the player chooses.

The disadvantage of this approach is that there is a chance — a 31%
chance, as it turns out — that your character is going suck.

Comparing Ability Scores

One way to decide if a character’s ability scores suck is to look at
the total of the six ability score modifiers.

Ability Score

Modifier

15

+2

14

+2

13

+1

12

+1

10

0

8

-1

Total

+5

For the official, non-random scores the total of the ability score
modifiers is +5.

How Good Are Random Ability Scores?

For a randomly generated character, the average sum of the six ability
score modifiers is 5.24, which corresponds nicely to the +5 total for
the scores 15, 14, 13, 12, 10, and 8.

The following figure shows the probability distribution of the sum of
the six ability score modifiers compared to rolling 3d6.2

Unfortunately, there is a decent chance (31%) that a randomly
generated character will have less than a +5 total for all six ability
score modifiers; in which case, the player would have been better off
assigning the scores 15, 14, 13, 12, 10, and 8.

Random vs. Assigned Ability Scores

If the choice is between either randomly rolling or assigning
abilitity scores, a player is probably better off assigning 15, 14,
13, 12, 10, and 8. There is a 59% chance you can do better, but also a
31% you will do worse.

The average result of 3d6 is 10.5 (+0 ability score modifier). The average result of the highest three of four 6-sided dice is 12.24 (+1 ability score modifier). The Python scripts dice.py and ability_scores.py were used to calculate these results. ↩